Three-way matrix navigation

p82.lisp

@@ -0,0 +1,29 @@
+(defparameter *matrix* (read-matrix-from-file "0082_matrix.txt"))
+
+(defparameter *directions* '((1 0)
+			     (0 1)
+			     (-1 0)))
+
+(defun path-sum-three-ways ()
+  (let* ((dimensions (array-dimensions *matrix*))
+	 (goal-column (1- (second dimensions)))
+	 (states (loop for r from 0 below (first dimensions)
+		       collect (cons (list r 0)
+				     (aref *matrix* r 0))))
+	 (visited (make-hash-table :test 'equal)))
+    (loop with sums = nil
+	  for state = (pop states)
+	  while state
+	  do (destructuring-bind (position . sum) state
+	       (setf (gethash position visited) t)
+	       (when (= (second position) goal-column)
+		 (push sum sums))
+	       (loop for offset in *directions*
+		     for new-position = (mapcar #'+ position offset)
+		     when (and (every #'in-bounds-p new-position dimensions)
+			       (not (gethash new-position visited)))
+		       do (push (cons new-position
+				      (+ sum (apply #'aref (cons *matrix* new-position))))
+				states))
+	       (setf states (sort states #'< :key #'cdr)))
+	  finally (return (apply #'min sums)))))